IIT JEE Mains (Offline) Question

Number of words formed using letters $S,M,A,L,L$ are $\frac{5!}{2!}=60$ . Now arranging the word in reverse order of alphabetical order we get

$SMLLA-60^{th}$

$SMLAL-59^{th}$

$SMALL-58^{th}$

Starting with $A$ , there are $4!=24$ possible words. But $12$ are repeated twice(because of $2$ L's) so there are $12$ words staring with $A$ .

Starting with $L$ . there are $4!=24$ possible words and none repeats.

Staring with $M$ , there are same number of words as $A$ which is $12$ .

Now Starting with $S$

There are $3$ words with second letter $A$ .

There are $6$ words with second letter $L$ .

The word $SMALL$ is the next words after this.

There have been $24+12+12+3+6=57$ till now.

Thus $SMALL$ is the $58^{th}$ word.